Question

Wolf packs tend to be large extended family groups that have a well-defined hunting territory. Wolves not in the pack are driven out of the territory or killed. In ecologically similar regions, is the size of an extended wolf pack related to size of hunting region? Using radio collars on wolves, the size of the hunting region can be estimated for a given pack of wolves. Let x represent the number of wolves in an extended pack and y represent the size of the hunting region in km²/1000. The following data are representative of one of the national parks.

x wolves	23	38	22	64	96
y km2/1000	7.37	12.14	8.17	15.35	16.83

(a) Verify that

Σx = 243,

Σy = 59.86,

Σx² = 15,769,

Σy² = 787.3168,

Σxy = 3408.65,

and

r ≈ 0.9

(b) Use a 1% level of significance to test the claim

ρ > 0.

(Use 2 decimal places.)

t
critical t

(d) Find the predicted size of the hunting region for an extended pack of 57 wolves. (Use 2 decimal places.)
13 km²/1000

(e) Find an 85% confidence interval for your prediction of part (d). (Use 1 decimal place.)

lower limit	km2/1000
upper limit	km2/1000

(f) Use a 1% level of significance to test the claim that

β > 0.

(Use 2 decimal places.)

t
critical t

.

(g) Find a 95% confidence interval for β and interpret its meaning in terms of drift rate. (Use 2 decimal places.)

lower limit
upper limit

Answer 1